I think you are remembering an older book (written in 1948), by A. E. van Vogt: The World of Null-A. The main characters starts the book by going to a city where a machine will be testing people (referred to as the 'Games') and selecting those with sufficient aptitude for further training/work on Venus.
Our hero (Gilbert Gosseyn) discovers that his memories are somehow false, and ends up on the run. Eventually he discovers that, should he be killed, he will wake up in a different copy of his body. Eventually he ends up on Venus and receives training in how to use a secondary brain that he possesses; it's this secondary brain that allows him to basically memorize objects and locations and move them from one memorized spot to another. (He peers thru a fence, memorizes a spot on the other side, and 'similiarizes' him there. At another point, he memorizes the output from a generator, and uses it as a weapon.)
It was followed by two other novels that expand on his abilities and past. Overall, the stories were mostly a vehicle to expose people to concepts of non-Aristotelian logic, as taught by Alfred Korzybski, via General Semantics.